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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

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Matrix representation of a certain algebra

The statement that this always CAN be done is called 'Ado's theorem'. One way to get an answer is to look for proofs of this theorem online. This blog post by Terrence Tao looks useful (but I didn't r …
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3 votes

Real representations of SO(n) and U(n)

The book by Broecker and tom Dieck (Representations of Compact groups, Springer Graduate Texts in Math) has a very useful section about real, complex and quaternionic representations and how to pass b …
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